1. Field of the Invention
The following description relates to a distributed Rivest Shamir Adleman (RSA) signature generation method in an ad-hoc network and a signature generation node. More particularly, the following description relates to a distributed RSA signature generation method which can use an RSA signature without interaction among nodes in a distributed RSA signature which distributes a function of a dealer node of a necessary certification authority for management of keys on the ad-hoc network, and a signature generation node.
2. Description of Related Art
Ubiquitous networking indicates that various networks are united based on an Internet Protocol (IP) to provide a seamless networking service to a user. When a ubiquitous service is desired to be realized by using wideband wireless network techniques in the present infrastructure base, there may be problems in that, as users  increase, a cell range decreases, and expansion of the network infrastructure is naturally required to overcome the decreases of the cell range. Subsequently, costs may be increased to maintain the network infrastructure and to build further network infrastructure. Also, there may be other problems in that, an entire network may be paralyzed when the network infrastructure is broken due to disasters such as war, fire, flooding, and so forth.
Mobile ad-hoc networks are required to reduce the costs for building the network infrastructure and to realize infrastructure-less wireless networking. Features of the mobile ad-hoc networks are as follows:                1. Self-organization: All nodes perform functions of a terminal and a router, and voluntarily configure a network;        2. Dynamic Topology: Topology of a network dynamically changes due to frequent movements of wireless terminal nodes;        3. Lack of Central Authority: There is neither a node functioning as a backbone, nor a node functioning as a certain node exist;        4. Lack of Association: It is not easy to control a network due to the lack of central authority feature, resulting in difficulties in controlling a node join and protection against malicious nodes;        5. No Synchronous Communication: Synchronous communication is impossible due to features of the dynamic topology. That is, synchronous communication is impossible when all nodes are simultaneously connected to a network; and        6. Bandwidth and Power Constraints: There is a limitation of network resources since the network is configured with wireless mobile devices.         
Basically, security requirements on the ad-hoc network are similar to security requirements on other networks. Conversely, in the case of an ad-hoc wireless network in a distributed computing environment such as a fully wireless ad-hoc network, it is inevitable to use encryption keys in unreliable circumstances. Therefore, a probability of relying on the encryption keys is increased. Accordingly, it is important to build a reliable relation between the encryption keys, and to distribute the encryption keys to the entire ad-hoc network. A distributed signature scheme based on a public key is one of the solutions that can solve the above problem.
In the distributed signature scheme, a message is encrypted using a secret key from a reliable certification authority, and the encrypted message is decrypted using a public key of the reliable certification authority, and a validity is verified.
However, all nodes on the network are required to perform a function of the reliable certification authority since the reliable certification authority does not exist in the ad-hoc network. The distributed signature scheme is based on secret sharing. Namely, the secret sharing indicates that secret information such as a secret key is shared based on a mathematical algorithm, and the secret information is restored using the shares. A Shamir method is one of the representative methods based on a polynomial interpolation for the secret sharing.
The polynomial interpolation is a type of algorithm. A unique ‘t-1’-degree polynomial can be defined when ‘t’ number of different points exist in a two-dimensional space, that is, after the ‘t-1’-degree polynomial is defined and points in the ‘t-1’-degree polynomial are distributed. When at least ‘t’ number of points are collected, an original polynomial can be found. The polynomial interpolation is suitable for the secret sharing. FIG. 1 is a diagram illustrating an example of a distributed RSA  signature method in the conventional art.
Specifically, among the nodes of an ad-hoc network, a signature generation node 100 requests neighbor nodes 101 and 102 for secret shares of the neighbor nodes 101 and 102. The neighbor nodes 101 and 102 then transmit their own secret shares to the signature generation node 100. Subsequently, the signature generation node 100 may generate the RSA signature using the secret shares of the neighbor nodes 101 and 102.
However, in the conventional art, the Shamir's distributed RSA signature generation method has a problem in that, at least ‘t’ number of points, that is, at least ‘t’ number of nodes, are required to simultaneously exist when using the polynomial interpolation which means communication among shareholders having the ‘t’ number of points may occur, that is, interaction among the shareholders occur. Subsequently, a leak of information about the shareholders may occur.
FIG. 2 is a diagram illustrating an example for describing the interaction in the Shamir's distributed RSA signature method in the conventional art.
In order to communicate with a plurality of nodes of an ad-hoc network 200, that is, for an RSA signature, a new node 201 communicates with nodes 202 through 204 of the plurality of nodes. This is considered as essential communication, however, this is not considered as the interaction. The nodes 202 through 204, having received the request for the signature from the node 201, collect a partial signature generated by using the nodes' 202 through 204 own shares to generate a public key. Generally, identification (ID) information of the nodes 202 through 204 is required when generating the partial signature.
However, the conventional distributed RSA signature method has problems in  that, additional communication, such as collecting information of other nodes to generate the partial signature, may occur, that is, an interaction 205 may occur. This may cause a security problem. There is another problem in that, all nodes are required to simultaneously exist in an environment where topology frequently changes, similar to the ad-hoc network 200.
Accordingly, to address the above and other problems, a non-interactive distributed RSA signature method is required.